We measured the mean plane of the Kuiper Belt as a function of semimajor axis. For the classical Kuiper Belt as a whole (the nonresonant objects in the semimajor axis range 42-48au), we find a mean plane of inclination i_m_=1.8{deg}-0.4{deg}^+0.7{deg}^ and longitude of ascending node {Omega}m=77{deg}-14{deg}^+18{deg}^ (in the J2000 ecliptic-equinox coordinate system), in accord with theoretical expectations of the secular effects of the known planets. With finer semimajor axis bins, we detect a statistically significant warp in the mean plane near semimajor axes 40-42au. Linear secular theory predicts a warp near this location due to the {nu}18 nodal secular resonance; however, the measured mean plane for the 40.3-42au semimajor axis bin (just outside the {nu}18) is inclined ~13{deg} to the predicted plane, a nearly 3{sigma} discrepancy. For the more distant Kuiper Belt objects of semimajor axes in the range 50-80au, the expected mean plane is close to the invariable plane of the solar system, but the measured mean plane deviates greatly from this: it has inclination i_m_=9.1{deg}-3.8{deg}^+6.6{deg}^ and longitude of ascending node {Omega}m=227{deg}-44{deg}^+18{deg}^. We estimate this deviation from the expected mean plane to be statistically significant at the ~97%-99% confidence level. We discuss several possible explanations for this deviation, including the possibility that a relatively close-in (a<~100au), unseen, small planetary-mass object in the outer solar system is responsible for the warping.